Note that, differently from the BOLS procedure of [1]}, which is computed in batches, the AW-AIPW approach is computed recursively after each new observation \(i\)  in each step \(t\) . In a general batched setting this means that we perform an estimation at each point \(t^{\prime } = 0,\dots , nT\) . Such requirement implies a computational cost much higher compared to both BOLS-based Z-test and the AP-test. Note that this is not only because of the need of computing the AW-AIPW for each \(t^{\prime } \in [0, nT]\)  (compared to the \(t \in [0, T]\)  of the other approaches), but also because the computation of the AW-AIPW estimator involves the estimation of the augmented reward model part (i.e., \(\hat{m}_{t,\cdot }\) ), and the adaptive weights (\(h_{t,\cdot }\) ), in addition to the IPW estimator.
